Vedic mathematics is an ancient system that allows for instant mental calculations of various mathematical problems through simple techniques. Some key techniques include using vertical and crosswise multiplication to avoid memorizing full multiplication tables, squaring numbers ending in 5 by multiplying the first number by the "one more than" number, and methods for multiplication, division, time conversions, temperature conversions, and unit conversions that reduce steps compared to standard algorithms. Vedic mathematics aims to help students solve problems more quickly, reduce memorization burden, and increase concentration through its unique calculation rules and principles.